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Formula
Calculate the value
$\sqrt{ \left( \sqrt{ 2 } -1 \right) ^{ 2 } } - \sqrt{ \left( 1- \sqrt{ 2 } \right) ^{ 2 } }$
$0$
Calculate the value
$\sqrt{ \left ( \sqrt{ 2 } - 1 \right ) ^ { \color{#FF6800}{ 2 } } } - \sqrt{ \left ( 1 - \sqrt{ 2 } \right ) ^ { 2 } }$
 Organize as the power is written in the radical sign, and the root exponent and the exponent are the same 
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } - \sqrt{ \left ( 1 - \sqrt{ 2 } \right ) ^ { 2 } }$
$\sqrt{ 2 } - 1 - \sqrt{ \left ( 1 - \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Organize as the power is written in the radical sign, and the root exponent and the exponent are the same 
$\sqrt{ 2 } - 1 - \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right )$
$\sqrt{ 2 } - 1 \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \left ( 1 - \sqrt{ 2 } \right ) \right )$
 Simplify Minus 
$\sqrt{ 2 } - 1 + 1 - \sqrt{ 2 }$
$\sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } - \sqrt{ 2 }$
 Remove the two numbers if the values are the same and the signs are different 
$\sqrt{ 2 } - \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } }$
 Remove the two numbers if the values are the same and the signs are different 
$0$
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